To help us enquire into this question, I showed a few different ways we can visually show fraction number sums. After drawing a different image, the children had some time to think and then shared their thoughts of the possibilities the picture might represent:
I also shared a student's really creative visualising idea that he had created earlier in the week:
So many different possibilities emerged from each image and we found that really fascinating how we could see them from such different perspectives.
To find out why visualising and creative thinking is important in mathematical thinking, we partnered up and had choices of different fraction word problems to solve. With mini whiteboards, each partner created a way to visualise the word problem. They then shared and discussed their creative ideas. They then solved the word problem numerically to see if it matched their visual.
The discussions generated amongst the partners were incredibly engaging and provoking deep thinking and challenges.
Regardless of each student's level of understanding fractions, each child's thinking was challenged and everyone really enjoyed the ideas bot they and their partners were able to create.
Some sample ideas:
After partners shared some visualising ideas with other groups, we then spent some time reflecting on what we had learnt about our enquiry question and then shared our ideas as a whole class:
Some really important discoveries were made today about mathematical thinking and many agreed that the activity helped them to see maths from a completely new perspective.
A lot of thinking had changed in our class and we are all strongly believed that visualising and creativity are really key components of mathematical thinking.